It depends. If you're looking to get a retro rig, I'd work out what the latest year of games I'd really want to play is and then get hardware from around that era.
In my case it'd probably be Escape From Monkey Island, which uses an updated version of Grim Fandango's engine and was released in 2001. So I'd get hardware that was prevalent in 2001, and indeed back in 2001 I could play Grim Fandango and all the older LucasArts classics very nicely with anti-aliasing and all.
I think at the time I was using a Pentium of some kind clocked at 1.2GHz, a GeForce 2 MX, and about 512mb of RAM. I might be thinking of my slightly newer machine with the processor/RAM, but I'm fairly certain on the graphics card.
While I'm surprised the 2x2 option isn't there and will look into it for my other post (it may have been renamed or further hidden), if you're getting other problems then it is indeed probably worth building an older machine. I'm guessing it'd be incredibly inexpensive to do so.
Although with that said, processors and RAM haven't fundamentally changed that much over the years unless you're using a 64-bit operating system, so it might be your graphics card and operating system that're contributing mostly to the problems.
What I'd do as a first step is buy a GeForce 2, make sure you're using very old drivers (newer ones will work but as Du Man's article points out, support for old games diminishes with time; for best results you want drivers that were used in 2001) and dual boot into Windows 98. You can then use the device manager to disable/enable the other graphics card in each operating system. This is, of course, assuming you have a spare AGP or PCI slot (the GeForce 2 came as both). If this fails then you can then go ahead and buy the remaining hardware needed.